The first Indemonstrable Principle

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In our contemporary world markedly influenced by a relativistic mentality, the existence of a first indemonstrable principle is, if not explicitly denied, at least considered irrelevant. This fact, however, makes all the more necessary, the explaining of how human beings do attain knowledge of the truth embodying the powerful principle called the first indemonstrable principle.

The first indemonstrable principle is also known as the principle of non-contradiction. The famous Polish logician Jan Lukasiewicz calls it simply the “law of contradiction” to mean that this is the principle on which one falls into contradiction.

We learn about the principle of non-contradiction when we study logic. In symbolic, formal, and material logic, non-contradiction is considered to be the law of thought.

In his well known essay “Aristotle on the Law of Contradiction” (published in “Articles on Aristotle,” vol. 3, ed. J. Barnes, M. Schofield, and R.Sorabji, London: Duckworth, 1979, pp. 50-62), Lukasiewicz declares that the first indemonstrable principle extends to the realms of ontology, logic, and psychology.

In ontological terms, according to Lukasiewicz, the first principle is as follows: “The same property cannot belong and not belong to a single subject at the same time.” In logical terms Lukasiewicz takes the first indemonstrable principle to mean that “Two contradictory sentences cannot be true at the same time.” And in psychological terms Lukasiewicz reports the following expression for the first principle: “If beliefs corresponding to contradictory sentences are contrary to one another, it is evident that the same person cannot at the same time believe the same thing to be and not to be. For if a man were mistaken on this point he would hold contrary beliefs at the same time.”

Lukasiewicz attributed to Aristotle the above expressions of the first indemonstrable principle. However, influenced by the development of symbolic logic and analytic philosophy, Lukasiewicz went on to affirm that for existence-free objects, such as numbers, or mathematical entities, and logical objects, the law of non-contradiction is not necessarily “the highest principle of every proof.” And in a similar manner, influenced by the philosophical development of phenomenology, Lukasiewicz went on to affirm that “the psychological law of contradiction is a thesis of doubtful truth; it is not yet established.” Lukasiewicz then concludes that the law of non-contradiction can be considered “first” only in the ontological realm.

For Aristotle, in fact, the principle of non-contradiction is above all the law of the real. Aristotle taught that we come to know the principle of non-contradiction through the experience of the world. For Aristotle, propositions refer to real things. For Aristotle, logic predication refers to the real inherence of qualities in subjects. And for Aristotle, names refer to what they mean.

Non-contradiction is particularly visible in nature. Darkness cannot coexist with light in the same room; in the presence of light, darkness disappears. Likewise, through chemistry we learn that an acidic water-soluble substance cannot coexist with a basic water-soluble substance in water in the same container; they neutralize each other. For ontological facts such as these, the law of non-contradiction is as rigorous as mathematical statements. It is in the realm of the ontological that the law of non-contradiction functions as a first indemonstrable principle.

Aristotle himself, in his “Metaphysics” (IV, 4 and XI, 5), gives an answer to those who foolishly attempt to negate the principle of non-contradiction. Aristotle says:

“In order to deny this principle, one has to reject all meaning in language. If ‘man’ were the same as ‘non-man’, it would not, in fact, mean anything at all. Any word would signify all things and would not, therefore, denote anything; everything would be the same. Consequently, all communication or understanding between persons would be impossible. Thus, whenever anyone says a word, he is already acknowledging the principle of non-contradiction, since he undoubtedly wants the word to mean something definite and distinct from its opposite. Otherwise, he would not even speak. Anyone who rejects this first principle should behave like a plant, since even animals move in order to attain an objective which they prefer over others, as when they seek food. Besides, denying this principle in fact implies accepting it, since in rejecting it, a person acknowledges that affirming and denying are not the same. If a person maintains that the principle of non-contradiction is false, he already admits that being true and being false are not the same, thereby accepting the very principle he wishes to eliminate.”

In conclusion, we human beings need to employ our mind and logic, as well as emotions and feelings in the process of searching and discerning the truth, or in the expression of Jacques Maritain, we must “distinguish in order to discern.” As said, in logical terms the first indemonstrable principle means that two opposing sentences cannot be true and untrue at the same time.

In psychological terms the same person cannot at the same time believe the same thing to be and not to be (unless in abnormal circumstances). It is not possible to predicate of the same thing, at the same time and in the same sense, the absence and the presence of the same fixed quality. Hence we aim to distinguish light from darkness, and/or right from wrong and similar things by using our mind and logic. This is the pathway to discern the truth.